# Find the Inverse y=-4x^2-2 Interchange the variables.
Solve for .
Rewrite the equation as .
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify each term.
Move the negative in front of the fraction.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Move the negative in front of the fraction.
Take the square root of both sides of the equation to eliminate the exponent on the left side.
The complete solution is the result of both the positive and negative portions of the solution.
Simplify the right side of the equation.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Multiply and .
Multiply by .
Combine the numerators over the common denominator.
Rewrite as .
Factor the perfect power out of .
Factor the perfect power out of .
Rearrange the fraction .
Reorder and .
Rewrite as .
Pull terms out from under the radical.
One to any power is one.
Combine and .
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the to find the first solution.
Next, use the negative value of the to find the second solution.
The complete solution is the result of both the positive and negative portions of the solution.
Solve for and replace with .
Replace the with to show the final answer.
Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the numerator.
Multiply by .
Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Since , is the inverse of .
Find the Inverse y=-4x^2-2     